Is (1-sin(x))/(1-csc(x))=-sin(x) ?

The answer to whether (1-sin(x))/(1-csc(x))=-sin(x) is True

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prove (1-sin(x))/(1-csc(x))=-sin(x)

prove

\frac{1 - sin ( x )}{1 - csc ( x )} = - sin (x)

True

Solution steps

\frac{1 - sin ( x )}{1 - csc ( x )} = - sin (x)

Manipulating left side

\frac{1 - sin ( x )}{1 - csc ( x )}

Express with sin, cos

= - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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cos (a) tan (a) = sin (a)

sin (\frac{π}{6}) = \frac{1}{2}

cot (2 x) = \frac{1}{2} cot (x) - \frac{1}{2} tan (x)

(sin (t) - cos (t))^{2} = 1 - sin (2 t)

Is (1-sin(x))/(1-csc(x))=-sin(x) ?
The answer to whether (1-sin(x))/(1-csc(x))=-sin(x) is True